Complete_Fermi–Dirac_integral
Complete Fermi–Dirac integral
Mathematical integral
In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is defined by
This equals
where is the polylogarithm.
Its derivative is
and this derivative relationship is used to define the Fermi-Dirac integral for nonpositive indices j. Differing notation for appears in the literature, for instance some authors omit the factor . The definition used here matches that in the NIST DLMF.